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Edgar Allan Poe was a highly literate man who had enrolled in the University of Virginia, at a time when few people completed grade school, never mind high school, or enrolled in college.
"Collegiate" is a requirement for being an officer in the U.S. army today, and even in those days, was extremely helpful. A college professor of rhetoric named Joshua Chamberlain was enrolled as a Lt. Colonel, and late promoted to Colonel and beyond. He started with no battlefield experience, but a lot of "book knowledge" about "refusing the flank" that enabled him to successfully lead his troops at Gettysburg.
At any rate, Poe enrolled in West Point after he left the army, and more to the point, was seen as "officer" material even before he left, despite his young age. His promotion to Sergeant Major was basically a "down payment" on this.